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B1322
Title: Statistics for SPDEs based on discrete observations Authors:  Florian Hildebrandt - University of Hamburg (Germany)
Mathias Trabs - Karlsruhe Institute of Technology (Germany) [presenting]
Abstract: Stochastic partial differential equations (SPDEs) combine the ability of deterministic PDE models to describe complex mechanisms with the key feature of diffusion models, namely a stochastic signal which evolves within the system. While SPDEs have been intensively studied in stochastic analysis, their statistical theory is still at its beginnings. We study parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension observing the solution field on a discrete grid in a fixed bounded domain. In particular, we discuss central limit theorems for realized quadratic variations based on temporal and spatial increments as well as on double increments in time and space in an infill asymptotic regime in both coordinates.